Factorize:
(i)`16 a^2-(25)/(4a^2)`
(ii) `16 a^2b-b/(16 a^2)`
(iii)`100(x+y)^2-81\ (a+b)^2`
(iv)`(x-1)^2-(x-2)^2`

Explanation

using identities `(a^2-b^2)=(a-b)(a+b)`
(i)`16 a^2-(25)/(4a^2)`
`=(4a+(5)/2a)(4a-(5)/2a)`

(ii)`16 a^2b-b/(16a^2)`
`=b{(4a)^2−(14a)^2}`
`=b(4a+14a)(4a−14a)`

(iii)`100(x+y)^2-81 (a+b)^2`
`={10(x+y)}^2–{9(a+b)}^2`
`={10(x+y)+9(a+b)}{10(x+y)–9(a+b)}`
`=(10x+10y+9a+9b)(10x+10y–9a–9b)`

(iv)`(x-1)^2-(x-2)^2`
`={(x–1)+(x–2)}{(x–1)–(x–2)}`
`=(2x–3)(x–1–x+2)`
`=(2x–3)xx1`
`=2x–3`